Question

Add the following polynomials, then place the answer in the proper location on the grid. Write your answer in descending powers of x.
x 4 -3x + 1, 4x 2 - 2x + 8, and x 3 - 9

Answer 1

The addition of the polynomials x⁴ - 3x + 1, 4x² - 2x + 8, x³ - 9 in descending powers of x is x⁴ + x³ + 4x² - 5x.

Polynomial

• x⁴ - 3x + 1
• 4x² - 2x + 8
• x³ - 9

Adding the polynomial

(x⁴ - 3x + 1) + (4x² - 2x + 8) + (x³ - 9)

• Open parenthesis

= x⁴ - 3x + 1 + 4x² - 2x + 8 + x³ - 9

• Collect like terms in descending powers

= x⁴ + x³ + 4x² - 3x - 2x + 1 + 8 - 9

= x⁴ + x³ + 4x² - 5x

Therefore, the addition of the polynomials x⁴ - 3x + 1, 4x² - 2x + 8, x³ - 9 in descending powers of x is x⁴ + x³ + 4x² - 5x.

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